(\partial)/(\partial t)(sech^2(x-t))

解

\frac{\partial}{\partial t} (sech^{2} (x - t))

2 sech^{2} (x - t) tanh (x - t)

解答ステップ

\frac{\partial}{\partial t} (sech^{2} (x - t))

x

を定数として扱う

連鎖法則を適用:

2 sech (x - t) \frac{\partial}{\partial t} (sech (x - t))

= 2 sech (x - t) \frac{\partial}{\partial t} (sech (x - t))

\frac{\partial}{\partial t} (sech (x - t)) = sech (x - t) tanh (x - t)

= 2 sech (x - t) sech (x - t) tanh (x - t)

簡素化

2 sech (x - t) sech (x - t) tanh (x - t) : 2 sech^{2} (x - t) tanh (x - t)

= 2 sech^{2} (x - t) tanh (x - t)